Elastic Stars in General Relativity: II. Radial perturbations

We study radial perturbations of general relativistic stars with elastic matter sources. We find that these perturbations are governed by a second order differential equation which, along with the boundary conditions, defines a Sturm-Liouville type problem that determines the eigenfrequencies. Although some complications arise compared to the perfect fluid case, leading us to consider a generalisation of the standard form of the Sturm-Liouville equation, the main results of Sturm-Liouville theory remain unaltered. As an important consequence we conclude that the mass-radius curve for a one-parameter sequence of regular equilibrium models belonging to some particular equation of state can be used in the same well-known way as in the perfect fluid case, at least if the energy density and the tangential pressure of the background solutions are continuous. In particular we find that the fundamental mode frequency has a zero for the maximum mass stars of the models with solid crusts considered in Paper I of this series.Comment: 22 pages, no figures, final version accepted for publication in Class. Quantum Grav. The treatment of the junction conditions has been improve

Mutual information in random Boolean models of regulatory networks

The amount of mutual information contained in time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating show that as the number of network nodes N approaches infinity, the quantity N exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of N is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.Comment: 11 pages, 6 figures; Minor revisions for clarity and figure format, one reference adde

Phospholipid precursors of prostaglandins

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33093/1/0000479.pd

Relativistic mechanics of neutron superfluid in (magneto) elastic star crust

At densities below the neutron drip threshold, a purely elastic solid model (including, if necessary, a frozen-in magnetic field) can provide an adequate description of a neutron star crust, but at higher densities it will be necessary to allow for the penetration of the solid lattice by an independently moving current of superfluid neutrons. In order to do this, the previously available category of relativistic elasticity models is combined here with a separately developed category of relativistic superfluidity models in a unified treatment based on the use of an appropriate Lagrangian master function. As well as models of the purely variational kind, in which the vortices flow freely with the fluid, such a master function also provides a corresponding category of non-dissipative models in which the vortices are pinned to the solid structure

Exploring the potential of ChatGPT as a supplementary tool for providing orthopaedic information

Purpose: To investigate the potential use of large language models (LLMs) in orthopaedics by presenting queries pertinent to anterior cruciate ligament (ACL) surgery to generative pre-trained transformer (ChatGPT, specifically using its GPT-4 model of March 14th 2023). Additionally, this study aimed to evaluate the depth of the LLM’s knowledge and investigate its adaptability to different user groups. It was hypothesized that the ChatGPT would be able to adapt to different target groups due to its strong language understanding and processing capabilities. Methods: ChatGPT was presented with 20 questions and response was requested for two distinct target audiences: patients and non-orthopaedic medical doctors. Two board-certified orthopaedic sports medicine surgeons and two expert orthopaedic sports medicine surgeons independently evaluated the responses generated by ChatGPT. Mean correctness, completeness, and adaptability to the target audiences (patients and non-orthopaedic medical doctors) were determined. A three-point response scale facilitated nuanced assessment. Results: ChatGPT exhibited fair accuracy, with average correctness scores of 1.69 and 1.66 (on a scale from 0, incorrect, 1, partially correct, to 2, correct) for patients and medical doctors, respectively. Three of the 20 questions (15.0%) were deemed incorrect by any of the four orthopaedic sports medicine surgeon assessors. Moreover, overall completeness was calculated to be 1.51 and 1.64 for patients and medical doctors, respectively, while overall adaptiveness was determined to be 1.75 and 1.73 for patients and doctors, respectively. Conclusion: Overall, ChatGPT was successful in generating correct responses in approximately 65% of the cases related to ACL surgery. The findings of this study imply that LLMs offer potential as a supplementary tool for acquiring orthopaedic knowledge. However, although ChatGPT can provide guidance and effectively adapt to diverse target audiences, it cannot supplant the expertise of orthopaedic sports medicine surgeons in diagnostic and treatment planning endeavours due to its limited understanding of orthopaedic domains and its potential for erroneous responses. Level of evidence: V

Energy dependent counting statistics in diffusive superconducting tunnel junctions

We present an investigation of the energy dependence of the full charge counting statistics in diffusive normal-insulating-normal-insulating-superconducting junctions. It is found that the current in general is transported via a correlated transfer of pairs of electrons. Only in the case of strongly asymmetric tunnel barriers or energies much larger than the Thouless energy is the pair transfer uncorrelated. The second cumulant, the noise, is found to depend strongly on the applied voltage and temperature. For a junction resistance dominated by the tunnel barrier to the normal reservoir, the differential shot noise shows a double peak feature at voltages of the order of the Thouless energy, a signature of an ensemble averaged electron-hole resonance.Comment: 8 pages, 5 figure

Proximity Effect and Multiple Andreev Reflections in Chaotic Josephson junctions

We study the dc-current transport in a voltage biased superconductor-chaotic dot-superconductor junction with an induced proximity effect(PE) in the dot. It is found that for a Thouless energy $E_{Th}$ of the dot smaller than the superconducting energy gap $\Delta$, the PE is manifested as peaks in the differential conductance at voltages of order $E_{Th}$ away from the even subharmonic gap structures $eV \approx 2(\Delta\pm E_{Th})/2n$. These peaks are insensitive to temperatures $kT \ll \Delta$ but are suppressed by a weak magnetic field. The current for suppressed PE is independent of $E_{Th}$ and magnetic field and is shown to be given by the Octavio-Tinkham-Blonder-Klapwijk theory.Comment: 4 pages, 3 figure

Observation of supercurrent enhancement in SNS junctions by non-equilibrium injection into supercurrent carrying bound Andreev states

We report for the first time enhancement of the supercurrent by means of injection in a mesoscopic three terminal planar SNSNS device made of Al on GaAs. When a current is injected from one of the superconducting Al electrodes at an injection bias $V=\Delta(T)/e$, the DC Josephson current between the other two superconducting electrodes has a maximum, giving evidence for an enhancement due to a non-equilibrium injection into bound Andreev states of the underlying semiconductor. The effect persists to temperatures where the equilibrium supercurrent has vanished.Comment: 7 pages + 3 figures. Resubmitted to Phys. Rev. Lett. Contents change

Investigating child participation in the everyday talk of a teacher and children in a preparatory year

In early years research, policy and education, a democratic perspective that positions children as participants and citizens is increasingly emphasized. These ideas take seriously listening to children’s opinions and respecting children’s influence over their everyday affairs. While much political and social investment has been paid to the inclusion of participatory approaches little has been reported on the practical achievement of such an approach in the day to day of early childhood education within school settings. This paper investigates talk and interaction in the everyday activities of a teacher and children in an Australian preparatory class (for children age 4-6 years) to see how ideas of child participation are experienced. We use an interactional analytic approach to demonstrate how participatory methods are employed in practical ways to manage routine interactions. Analysis shows that whilst the teacher seeks the children’s opinion and involves them in decision-making, child participation is at times constrained by the context and institutional categories of “teacher” and “student” that are jointly produced in their talk. The paper highlights tensions that arise for teachers as they balance a pedagogical intent of “teaching” and the associated institutional expectations, with efforts to engage children in decision-making. Recommendations include adopting a variety of conversational styles when engaging with children; consideration of temporal concerns and the need to acknowledge the culture of the school